Current methods dealing with non-rigid augmented reality only provide an augmented view when the topology of the tracked object is not modified, which is an important limitation. In this paper we solve this shortcoming by introducing a method for physics-based non-rigid augmented reality. Singularities caused by topological changes are detected by analyzing the displacement field of the underlying deformable model. These topological changes are then applied to the physics-based model to approximate the real cut. All these steps, from deformation to cutting simulation, are performed in real-time. This significantly improves the coherence between the actual view and the model, and provides added value.